Trump signed the bill under bipartisan pressure from the Congress amid a sweeping federal probe investigating whether officials in Trump’s election campaign had coordinated with Russia to help the Republican president defeat his Democratic rival Hillary Clinton in last year’s election.

Trump's desire for better ties with Moscow is an open secret, now reversed by accusations from US intelligence agencies that Russia operated a series of high-profile cyber attacks to change the outcome of the November 8 presidential election in favor of Trump.

Trump warned Thursday that Washington's ties with Moscow were at a “very dangerous low," and blamed Congress for the situation, a day after he reluctantly signed into law a sanctions bill against Russia.

"Our relationship with Russia is at an all-time & very dangerous low," Trump said in a Twitter post. "You can thank Congress.”

Trump said in a statement on Wednesday that the bill was flawed and some of its provisions stood at variance with the US Constitution.

The Russians, however, said Moscow would reserve its right to take retaliatory measures against the bill signed by President Trump.

The US slapped sanctions on Russia over Moscow's alleged role in the eastern Ukraine crisis, and also for allegedly tampering in the 2016 US presidential election in favor of Trump.